## Section5.1Degree of Freedom

Degrees of freedom refers to the number of independent parameters or values required to specify the state of an object.

The state of a particle is completely specified by its location in space, while the state of a rigid body includes its location in space and also its orientation.

Two-dimensional rigid bodies in the $$xy$$ plane have three degrees of freedom. Position can be characterized by the $$x$$ and $$y$$ coordinates of a point on the object, and orientation by angle $$\theta_z$$ about an axis perpendicular to the plane. The complete movement of the body can be defined by two linear displacements $$\Delta x$$ and $$\Delta y\text{,}$$ and one angular displacement $$\Delta \theta_z\text{.}$$

Three-dimensional rigid bodies have six degrees of freedom, which can be specified with three orthogonal coordinates $$x, y$$ and $$z\text{,}$$ and three angles of rotation, $$\theta_x, \theta_y$$ and $$\theta_z\text{.}$$ Movement of the body is defined by three translations $$\Delta x\text{,}$$ $$\Delta y$$ and $$\Delta z\text{,}$$ and three rotations $$\Delta \theta_x\text{,}$$ $$\Delta \theta_y$$ and $$\theta_z\text{.}$$